Large-eddy simulations of turbulent flows using the high-order FR/CPR method

Abstract

Large eddy simulation (LES) was originally proposed for simulating atmospheric flows and then has become one of the most successful methodologies for turbulence simulation for its good balance between accuracy and cost. In LES, energetic scales are resolved while the small equilibrium scales are modeled by the sub-grid scale(SGS) stress models. The resolution of the wide spectrum of the energetic scales is a big challenge for numerical methods. High-order methods are very promising in LES for its low dissipation and dispersion errors. For smooth turbulent flow, high-order methods have the potential to achieve high accuracy at lower cost than lower order methods. This thesis presents the investigation of the performance of different LES sub-grid scale stress (SGS) models with the high-order flux reconstruction or the correction procedure via reconstruction( FR/CPR) method. A mathematical analysis of scale similarity is conducted and presented as well. In addition, numerical schemes’ behavior in nonlinear wave propagation is studied and presented. The computationa of discontinuities, such as shocks, is another challenge to the numerical methods. In the simulation of shocks, non-physical oscillations can occur at the discontinuities and lead to divergence. The situation is worse for high-order methods. This thesis also presents a new flux limiter for the FR/CPR method. The new technique shows good properties, convergence for steady problems and accuracy preserving for vortex dominated flows. It is very promising in handling shock and turbulence interaction problems.